单重场论与Flato-Fronsdal偶极方程
Singleton field theory and Flato - Fronsdal dipole equation
摘要：
我们研究了方程$(\triangle -λ)ϕ= 0$和$(\triangle -λ)^2ϕ= 0$在$d$维Anti deSitter空间的覆盖空间$CAdS_d$上的全局坐标下的解，这些解受各种边界条件的约束，并且它们与$\widetilde{SO}(d-1,2)$的酉不可约表示有关。在空间无穷远处的“消失通量”边界条件导致了$CAdS_d$的标准量子化方案，其中二阶和四阶方程的解是等价的。要包括实现单点酉表示的领域在大量的$CAdS_d$之一，以放松边界条件，从而允许非平凡空间的解决方案的偶极子方程称为古普塔-布莱德利三重态。我们得到明确的表达式的模式的Gupta-Bleetheit三重态和相应的两点函数。为了避免负能态，还必须在偶极方程的解的空间中引入附加约束。
英文摘要：
We study solutions of the equations $(\triangle -λ)ϕ= 0$ and $(\triangle -λ)^2ϕ= 0$ in global coordinates on the covering space $CAdS_d$ of the $d$-dimensional Anti de-Sitter space subject to various boundary conditions and their connection to the unitary irreducible representations of $\widetilde{SO}(d-1,2)$. The ``vanishing flux'' boundary conditions at spatial infinity lead to the standard quantization scheme for $CAdS_d$ in which solutions of the second- and the fourth-order equations are equivalent. To include fields realizing the singleton unitary representation in the bulk of $CAdS_d$ one has to relax the boundary conditions thus allowing for the nontrivial space of solutions of the dipole equation known as the Gupta - Bleuler triplet. We obtain explicit expressions for the modes of the Gupta - Bleuler triplet and the corresponding two-point function. To avoid negative-energy states one must also introduce an additional constraint in the space of solutions of the dipole equation.
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